VSSI2p-Net: Physics-guided deep unfolding with L2p-norm and variation sparsity for EEG source imaging

Electroencephalogram (EEG) source imaging (ESI) is highly underdetermined, which poses a long-standing challenge in neuroimaging. Traditional methods typically rely on predefined priors to constrain the solution space; however, the need for manual parameter adjustments often makes it difficult to achieve optimal integration of prior information. Although recent deep learning methods can automatically update parameters in a data-driven manner, their black-box characteristics lead to a lack of interpretability and the need for extensive training sets. To integrate the advantages of these two types of methods, we propose a novel neural network model based on deep unfolding, called variation sparse source imaging network (VSSI 2 p -Net). Specifically, we introduce variation sparsity and ℓ 2 , p norm ( 0 < p < 1 ) regularization into the model of the ESI problem and utilize the Alternating Direction Method of Multipliers (ADMM) to iteratively solve this model. Furthermore, by mapping the iterative process into a neural network structure, the proposed VSSI 2 p -Net can optimize all parameters, including the critical p in ℓ 2 , p -norm and the variation sparsity operator, in an end-to-end manner with a reasonably sized training set. In this way, VSSI 2 p -Net achieves more flexible prior information integration while retaining the interpretability of traditional methods, so that a more accurate and efficient solution for ESI can be obtained. We compared the performance of VSSI 2 p -Net with several traditional baseline methods and state-of-the-art deep learning methods on synthetic and real datasets. The results show that VSSI 2 p -Net significantly outperforms existing methods in source localization accuracy, spatial range estimation, and imaging speed across various source configurations.